This paper studies the empirical performance of stochastic volatility models for twenty years of weekly exchange rate data. We concentrate on the effects of the distribution of the exchange rate innovations for parameter estimates and for estimates of the latent volatility series. We approximate the density of the log of exchange rate innovations by a mixture of normals. The major findings of the paper are that: (1) explicitly incorporating fat-tailed innovations increases the estimates of the persistence of volatility dynamics; (ii) estimates of the latent volatility series depend strongly on the estimation technique; (iii) the estimation error of the volatility time series is so large that finance applications to option pricing should be interpreted with care. We reach these conclusions using three different estimation techniques: quasi maximum likelihood, simulated EM, and a Bayesian procedure based on the Gibbs sampler.